RESUMO
Wavelets provide potentially useful quantum bases for coupled anharmonic vibrational modes in polyatomic molecules as well as many other problems. A single compact support wavelet family provides a flexible basis with properties of orthogonality, localization, customizable resolution, and systematic improvability for general types of one-dimensional and separable systems. While direct product wavelet bases can be used in coupled multidimensional problems, exponential scaling of basis size with dimensionality ultimately provides limits on the number of coupled modes that can be treated simultaneously in exact quantum calculations. The molecular self-consistent-field plus configuration-interaction method is used here in multimode wavelet calculations to reduce the basis size without sacrificing flexibility or the ability to systematically control errors. Both two-dimensional Cartesian coordinate and three-dimensional curvilinear coordinate systems are examined with wavelets serving as universal bases in each case. The first example uses standard Daubechies [Ten Lectures on Wavelets (SIAM, Philadelphia (1992)] wavelets for each mode and the second adapts symmlet wavelets to intervals for each of the curvilinear coordinates.
RESUMO
Multiwavelet bases have been shown recently to apply to a variety of quantum problems. There are, however, only a few multiwavelet families that have been defined to date. Chui-Lian-type symmetric and antisymmetric multiwavelets are derived here that equal and exceed the polynomial interpolating power of previously available examples. Adaptations to domain edges are made with a view to use in curvilinear coordinate molecular calculations. The new highest-order multiwavelet family is shown to provide uniformly better performance for (i) basis representation of terms such as 1r(2) in near approach to the singularity at r=0 and (ii) eigenvalue calculation of a bending Hamiltonian taken from a curvilinear model of the ground-state vibrations of nitrosyl chloride.
